[EM] Anyone got a good analysis on limitations of approval and range voting?

[Kristofer Munsterhjelm]

Jobst Heitzig wrote:
> Hello Kristofer,
> 
> you wrote:

>> You could probably devise a whole class of SEC-type methods. They would
>> go: if there is a consensus (defined in some fashion), then it wins -
>> otherwise, a nondeterministic strategy-free method is used to pick the
>> winner. The advantage of yours is that it uses only Plurality ballots.
> 
> The hard point is, I think, to define what actually a potential
> consensus option is. And here the idea was to say everything unanimously
> preferred to some benchmark outcome qualifies as potential consensus.
> The benchmark then cannot be any feasible option but must be a lottery
> of some options, otherwise the supporters of the single option would
> block the consensus. But which lottery you take as a benchmark could be
> discussed. I chose the Random Ballot lottery since it seems the most
> fair one and has all nice properties (strategy-freeness, proportional
> allocation of power).
> 
>> I suppose the nondeterministic method would have to be "bad enough" to
>> provide incentive to pick the right consensus, yet it shouldn't be so
>> bad as to undermine the process itself if the voters really can't reach
>> a consensus.
> 
> Although I can hardly imagine real-world situations in which no
> consensus option can be found (maybe be combining different decisions
> into one, or using some kind of compensation scheme if necessary).

That might be true for a consensus in general, but I was referring to 
the SEC method, where all it takes is for a single voter to submit a 
different consensus ballot than the rest.

>> Assume (for the sake of simplicity) that we can get ranked information
>> from the voters. What difference would a SEC with Random Pair make, with
>> respect to Random Ballot? 
> 
> This sounds interesting, but what exactly do you mean by Random Pair?
> Pick a randomly chosen pair of candidates and elect the pairwise winner
> of them? I will think about this...

Yes. The CW now has a greater chance to win - but note that it's not 
given that the CW will win, because if he's not picked as one of the 
pair candidates, he doesn't come into play at all.

>> It would lead to a better outcome if the
>> consensus fails, but so also make it more likely that the consensus does
>> fail. Or would it? The reasoning from a given participant's point of
>> view is rather: do I get something *I* would like by refusing to take
>> part in consensus -- not, does *society* get something acceptable.
> 
> I'm not sure I know what you mean here.

Well, I was thinking that the SEC method provides an incentive for 
people to reach a common consensus because the alternative, which is the 
random ballot, isn't very good. Any (random or deterministic) method 
that favors some group would lead to that group having less of an 
incentive to participate in the consensus process because they know 
they'll get something they'll like.

Therefore, I at first thought that even though Random Pair would provide 
a result more people would be happy with, it would make the voters less 
interested in actually finding a consensus because the alternative isn't 
so bad anymore. However, then I realized that any given voter, if he's 
at the point where he doesn't care about the consensus option, will not 
be deterred from such a line of thinking because the alternative is 
suboptimal for society, only if it is suboptimal in his point of view. 
That means that you could replace Random Ballot with Random Pair as long 
as the fairness (what you call proportional allocation of power) remains 
intact, because if the improvement in result lifts all the groups 
equally, there's no more incentive for some group to "cheat" with 
respect to any other.

There's also another way of looking at it, which I just saw now: my 
first idea was that you can't move to a lottery that gives consistently 
good results because that will diminish people's interest in determining 
a consensus. But if the lottery is both fair and provides good results, 
then who cares? The consensus option will only come into play if the 
people can explicitly agree on a choice that's better than the expected 
value of the lottery. If figuring out a consensus is worth it (much 
better than the lottery, relatively speaking), then people will care, 
otherwise they won't. Thus improving the lottery part of the method will 
improve the method in general - it'll make up the amount it no longer 
encourages people to determine the consensus, by just giving better results.